{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2001:34I4PW7ZSAB7ULOASDDWUZIXCZ","short_pith_number":"pith:34I4PW7Z","canonical_record":{"source":{"id":"quant-ph/0109004","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"quant-ph","submitted_at":"2001-09-02T14:58:46Z","cross_cats_sorted":["hep-th","math-ph","math.MP"],"title_canon_sha256":"a2334baf2f4ff06a0e287cb9943079da2c6a6d340c19e3fec1d299be57d8ed74","abstract_canon_sha256":"5d3b05e3c15adb00457be8aadefcc6693c0febc8e8e6f06237f1e335ab9b7551"},"schema_version":"1.0"},"canonical_sha256":"df11c7dbf99003fa2dc090c76a65171655d49780ed72b72677d4bb6eb1d4068f","source":{"kind":"arxiv","id":"quant-ph/0109004","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"quant-ph/0109004","created_at":"2026-07-04T14:45:41Z"},{"alias_kind":"arxiv_version","alias_value":"quant-ph/0109004v1","created_at":"2026-07-04T14:45:41Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.quant-ph/0109004","created_at":"2026-07-04T14:45:41Z"},{"alias_kind":"pith_short_12","alias_value":"34I4PW7ZSAB7","created_at":"2026-07-04T14:45:41Z"},{"alias_kind":"pith_short_16","alias_value":"34I4PW7ZSAB7ULOA","created_at":"2026-07-04T14:45:41Z"},{"alias_kind":"pith_short_8","alias_value":"34I4PW7Z","created_at":"2026-07-04T14:45:41Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2001:34I4PW7ZSAB7ULOASDDWUZIXCZ","target":"record","payload":{"canonical_record":{"source":{"id":"quant-ph/0109004","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"quant-ph","submitted_at":"2001-09-02T14:58:46Z","cross_cats_sorted":["hep-th","math-ph","math.MP"],"title_canon_sha256":"a2334baf2f4ff06a0e287cb9943079da2c6a6d340c19e3fec1d299be57d8ed74","abstract_canon_sha256":"5d3b05e3c15adb00457be8aadefcc6693c0febc8e8e6f06237f1e335ab9b7551"},"schema_version":"1.0"},"canonical_sha256":"df11c7dbf99003fa2dc090c76a65171655d49780ed72b72677d4bb6eb1d4068f","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-04T14:45:41.606561Z","signature_b64":"utrfCxjGTjL5WLfoFWvhBZ+Mno8c6J6QPC+f+0+/xA4LMFsJlw8VDC9580pzW/KGzq77ZZYQDvAjpYCn+LQKDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"df11c7dbf99003fa2dc090c76a65171655d49780ed72b72677d4bb6eb1d4068f","last_reissued_at":"2026-07-04T14:45:41.606101Z","signature_status":"signed_v1","first_computed_at":"2026-07-04T14:45:41.606101Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"quant-ph/0109004","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-04T14:45:41Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"yKH35Gyv2W/OC7IXwLoT/V2z03yEP5TQuJgtfCVLeYdjXoVBDNorBFVZI5LkOMy9AmpxmscudjPuwgjgqUeIDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-08T14:35:11.617897Z"},"content_sha256":"f6f92e334822f625c76208510dc4f6079093f13a7170ca9ca33952fad5c6d701","schema_version":"1.0","event_id":"sha256:f6f92e334822f625c76208510dc4f6079093f13a7170ca9ca33952fad5c6d701"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2001:34I4PW7ZSAB7ULOASDDWUZIXCZ","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Quantum Computing and Shor`s Factoring Algorithm","license":"","headline":"","cross_cats":["hep-th","math-ph","math.MP"],"primary_cat":"quant-ph","authors_text":"Igor V. Volovich","submitted_at":"2001-09-02T14:58:46Z","abstract_excerpt":"Lectures on quantum computing. Contents: Algorithms. Quantum circuits. Quantum Fourier transform. Elements of number theory. Modular exponentiation. Shor`s algorithm for finding the order. Computational complexity of Schor`s algorithm. Factoring integers. NP-complete problems."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"quant-ph/0109004","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/quant-ph/0109004/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-04T14:45:41Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"7skPHhE8gydc3mXV+UfXolbR2Y38sSOrVayaq1ZhqVYg6Mehuv+aALvs5ePsE0AXQWg/x3rRRUgD8sC/L0nEBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-08T14:35:11.618521Z"},"content_sha256":"2f04e532e118e839b0d47ee7e618bb18db95f32938e2e3908a473ae49ffdf037","schema_version":"1.0","event_id":"sha256:2f04e532e118e839b0d47ee7e618bb18db95f32938e2e3908a473ae49ffdf037"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/34I4PW7ZSAB7ULOASDDWUZIXCZ/bundle.json","state_url":"https://pith.science/pith/34I4PW7ZSAB7ULOASDDWUZIXCZ/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/34I4PW7ZSAB7ULOASDDWUZIXCZ/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-08-08T14:35:11Z","links":{"resolver":"https://pith.science/pith/34I4PW7ZSAB7ULOASDDWUZIXCZ","bundle":"https://pith.science/pith/34I4PW7ZSAB7ULOASDDWUZIXCZ/bundle.json","state":"https://pith.science/pith/34I4PW7ZSAB7ULOASDDWUZIXCZ/state.json","well_known_bundle":"https://pith.science/.well-known/pith/34I4PW7ZSAB7ULOASDDWUZIXCZ/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2001:34I4PW7ZSAB7ULOASDDWUZIXCZ","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"5d3b05e3c15adb00457be8aadefcc6693c0febc8e8e6f06237f1e335ab9b7551","cross_cats_sorted":["hep-th","math-ph","math.MP"],"license":"","primary_cat":"quant-ph","submitted_at":"2001-09-02T14:58:46Z","title_canon_sha256":"a2334baf2f4ff06a0e287cb9943079da2c6a6d340c19e3fec1d299be57d8ed74"},"schema_version":"1.0","source":{"id":"quant-ph/0109004","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"quant-ph/0109004","created_at":"2026-07-04T14:45:41Z"},{"alias_kind":"arxiv_version","alias_value":"quant-ph/0109004v1","created_at":"2026-07-04T14:45:41Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.quant-ph/0109004","created_at":"2026-07-04T14:45:41Z"},{"alias_kind":"pith_short_12","alias_value":"34I4PW7ZSAB7","created_at":"2026-07-04T14:45:41Z"},{"alias_kind":"pith_short_16","alias_value":"34I4PW7ZSAB7ULOA","created_at":"2026-07-04T14:45:41Z"},{"alias_kind":"pith_short_8","alias_value":"34I4PW7Z","created_at":"2026-07-04T14:45:41Z"}],"graph_snapshots":[{"event_id":"sha256:2f04e532e118e839b0d47ee7e618bb18db95f32938e2e3908a473ae49ffdf037","target":"graph","created_at":"2026-07-04T14:45:41Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/quant-ph/0109004/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Lectures on quantum computing. Contents: Algorithms. Quantum circuits. Quantum Fourier transform. Elements of number theory. Modular exponentiation. Shor`s algorithm for finding the order. Computational complexity of Schor`s algorithm. Factoring integers. NP-complete problems.","authors_text":"Igor V. Volovich","cross_cats":["hep-th","math-ph","math.MP"],"headline":"","license":"","primary_cat":"quant-ph","submitted_at":"2001-09-02T14:58:46Z","title":"Quantum Computing and Shor`s Factoring Algorithm"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"quant-ph/0109004","kind":"arxiv","version":1},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:f6f92e334822f625c76208510dc4f6079093f13a7170ca9ca33952fad5c6d701","target":"record","created_at":"2026-07-04T14:45:41Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"5d3b05e3c15adb00457be8aadefcc6693c0febc8e8e6f06237f1e335ab9b7551","cross_cats_sorted":["hep-th","math-ph","math.MP"],"license":"","primary_cat":"quant-ph","submitted_at":"2001-09-02T14:58:46Z","title_canon_sha256":"a2334baf2f4ff06a0e287cb9943079da2c6a6d340c19e3fec1d299be57d8ed74"},"schema_version":"1.0","source":{"id":"quant-ph/0109004","kind":"arxiv","version":1}},"canonical_sha256":"df11c7dbf99003fa2dc090c76a65171655d49780ed72b72677d4bb6eb1d4068f","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"df11c7dbf99003fa2dc090c76a65171655d49780ed72b72677d4bb6eb1d4068f","first_computed_at":"2026-07-04T14:45:41.606101Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-04T14:45:41.606101Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"utrfCxjGTjL5WLfoFWvhBZ+Mno8c6J6QPC+f+0+/xA4LMFsJlw8VDC9580pzW/KGzq77ZZYQDvAjpYCn+LQKDA==","signature_status":"signed_v1","signed_at":"2026-07-04T14:45:41.606561Z","signed_message":"canonical_sha256_bytes"},"source_id":"quant-ph/0109004","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:f6f92e334822f625c76208510dc4f6079093f13a7170ca9ca33952fad5c6d701","sha256:2f04e532e118e839b0d47ee7e618bb18db95f32938e2e3908a473ae49ffdf037"],"state_sha256":"8f6c68d25bc3ac67327cd39ec44bf67f120873d7142f9b6e29b8b521d0a9c44c"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ecU+zJfz14ZXsUIju3CSnhaU3YPSAJ/yGYNSkk6pKEXZzuAQ4XGup+uhPuMh9IL8y1BEsNSI8MjHK0KeBIUaDQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-08T14:35:11.623045Z","bundle_sha256":"ef1a9a1333c584c99e8c8a0e497036120c6ffca510d6fdc4d314673806da4d7b"}}